Absolutely, Whizzwang! There is an assumption here that will probably never happen in game, where all your cards (minus starting posse) are in the deck (or discard, and ready to be redrawn). It's technically possible, just very unlikely.

However, if you assume that all the cards in play, discard, and boot hill are in proportion to the original draw structure, it doesn't matter how many cards are left in the deck, as the odds will very roughly be the same. For instance, if you've played 15 cards into the discard and in play, we have to assume 5 are 2's, 5 are 3's, and 5 are 4's with the 16x3 deck, and likewise for the proportion of any other decks draw structure. Using the hypergeometric calculator on that situation, I got the same results within about 1% of the original number.

Using that as a base, a crafty player can scan what is in play/discard/boot hill and quickly make a rough estimate of the odds. Are lots more of the 'off value' cards still in the deck? This'll Hurt will have a higher chance of hurting. Etc etc

P.S. Please don't do this if you are a new player... you have enough things to remember already! We don't want peoples turns taking 5 minutes per action...